The Resource Lecture notes on regularity theory for the NavierStokes equations, Gregory Seregin
Lecture notes on regularity theory for the NavierStokes equations, Gregory Seregin
Resource Information
The item Lecture notes on regularity theory for the NavierStokes equations, Gregory Seregin represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of MissouriSt. Louis Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Lecture notes on regularity theory for the NavierStokes equations, Gregory Seregin represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of MissouriSt. Louis Libraries.
This item is available to borrow from 1 library branch.
 Summary
 The lecture notes in this book are based on the TCC (Taught Course Centre for graduates) course given by the author in Trinity Terms of 20092011 at the Mathematical Institute of Oxford University. It contains more or less an elementary introduction to the mathematical theory of the NavierStokes equations as well as the modern regularity theory for them. The latter is developed by means of the classical PDE's theory in the style that is quite typical for St Petersburg's mathematical school of the NavierStokes equations. The global unique solvability (wellposedness) of initial boundary value
 Language
 eng
 Extent
 1 online resource
 Contents

 Preface; Contents; 1. Preliminaries; 1.1 Notation; 1.2 Newtonian Potential; 1.3 Equation div u = b; 1.4 Necas Imbedding Theorem; 1.5 Spaces of Solenoidal Vector Fields; 1.6 Linear Functionals Vanishing on Divergence Free Vector Fields; 1.7 HelmholtzWeyl Decomposition; 1.8 Comments; 2. Linear Stationary Problem; 2.1 Existence and Uniqueness of Weak Solutions; 2.2 Coercive Estimates; 2.3 Local Regularity; 2.4 Further Local Regularity Results, n = 2, 3; 2.5 Stokes Operator in Bounded Domains; 2.6 Comments; 3. NonLinear Stationary Problem; 3.1 Existence of Weak Solutions
 3.2 Regularity of Weak Solutions3.3 Comments; 4. Linear NonStationary Problem; 4.1 Derivative in Time; 4.2 Explicit Solution; 4.3 Cauchy Problem; 4.4 Pressure Field. Regularity; 4.5 Uniqueness Results; 4.6 Local Interior Regularity; 4.7 Local Boundary Regularity; 4.8 Comments; 5. Nonlinear NonStationary Problem; 5.1 Compactness Results for NonStationary Problems; 5.2 Auxiliary Problem; 5.3 Weak LerayHopf Solutions; 5.4 Multiplicative Inequalities and Related Questions; 5.5 Uniqueness of Weak LerayHopf Solutions. 2D Case; 5.6 Further Properties of Weak LerayHopf Solutions
 Appendix A Backward Uniqueness and Unique ContinuationA. 1 CarlemanType Inequalities; A.2 Unique Continuation Across Spatial Boundaries; A.3 Backward Uniqueness for Heat Operator in Half Space; A.4 Comments; Appendix B LemarieRiesset Local Energy Solutions; B.1 Introduction; B.2 Proof of Theorem 1.6; B.3 Regularized Problem; B.4 Passing to Limit and Proof of Proposition 1.8; B.5 Proof of Theorem 1.7; B.6 Density; B.7 Comments; Bibliography; Index
 Isbn
 9789814623414
 Label
 Lecture notes on regularity theory for the NavierStokes equations
 Title
 Lecture notes on regularity theory for the NavierStokes equations
 Statement of responsibility
 Gregory Seregin
 Language
 eng
 Summary
 The lecture notes in this book are based on the TCC (Taught Course Centre for graduates) course given by the author in Trinity Terms of 20092011 at the Mathematical Institute of Oxford University. It contains more or less an elementary introduction to the mathematical theory of the NavierStokes equations as well as the modern regularity theory for them. The latter is developed by means of the classical PDE's theory in the style that is quite typical for St Petersburg's mathematical school of the NavierStokes equations. The global unique solvability (wellposedness) of initial boundary value
 Cataloging source
 N$T
 http://library.link/vocab/creatorDate
 1950
 http://library.link/vocab/creatorName
 Seregin, Gregory
 Dewey number
 515/.353
 Index
 index present
 LC call number
 QA377
 LC item number
 .S463 2014eb
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 http://library.link/vocab/subjectName

 NavierStokes equations
 Fluid dynamics
 MATHEMATICS
 MATHEMATICS
 Fluid dynamics
 NavierStokes equations
 Label
 Lecture notes on regularity theory for the NavierStokes equations, Gregory Seregin
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents

 Preface; Contents; 1. Preliminaries; 1.1 Notation; 1.2 Newtonian Potential; 1.3 Equation div u = b; 1.4 Necas Imbedding Theorem; 1.5 Spaces of Solenoidal Vector Fields; 1.6 Linear Functionals Vanishing on Divergence Free Vector Fields; 1.7 HelmholtzWeyl Decomposition; 1.8 Comments; 2. Linear Stationary Problem; 2.1 Existence and Uniqueness of Weak Solutions; 2.2 Coercive Estimates; 2.3 Local Regularity; 2.4 Further Local Regularity Results, n = 2, 3; 2.5 Stokes Operator in Bounded Domains; 2.6 Comments; 3. NonLinear Stationary Problem; 3.1 Existence of Weak Solutions
 3.2 Regularity of Weak Solutions3.3 Comments; 4. Linear NonStationary Problem; 4.1 Derivative in Time; 4.2 Explicit Solution; 4.3 Cauchy Problem; 4.4 Pressure Field. Regularity; 4.5 Uniqueness Results; 4.6 Local Interior Regularity; 4.7 Local Boundary Regularity; 4.8 Comments; 5. Nonlinear NonStationary Problem; 5.1 Compactness Results for NonStationary Problems; 5.2 Auxiliary Problem; 5.3 Weak LerayHopf Solutions; 5.4 Multiplicative Inequalities and Related Questions; 5.5 Uniqueness of Weak LerayHopf Solutions. 2D Case; 5.6 Further Properties of Weak LerayHopf Solutions
 Appendix A Backward Uniqueness and Unique ContinuationA. 1 CarlemanType Inequalities; A.2 Unique Continuation Across Spatial Boundaries; A.3 Backward Uniqueness for Heat Operator in Half Space; A.4 Comments; Appendix B LemarieRiesset Local Energy Solutions; B.1 Introduction; B.2 Proof of Theorem 1.6; B.3 Regularized Problem; B.4 Passing to Limit and Proof of Proposition 1.8; B.5 Proof of Theorem 1.7; B.6 Density; B.7 Comments; Bibliography; Index
 Control code
 894894804
 Dimensions
 unknown
 Extent
 1 online resource
 File format
 unknown
 Form of item
 online
 Isbn
 9789814623414
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number
 (OCoLC)894894804
 Label
 Lecture notes on regularity theory for the NavierStokes equations, Gregory Seregin
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents

 Preface; Contents; 1. Preliminaries; 1.1 Notation; 1.2 Newtonian Potential; 1.3 Equation div u = b; 1.4 Necas Imbedding Theorem; 1.5 Spaces of Solenoidal Vector Fields; 1.6 Linear Functionals Vanishing on Divergence Free Vector Fields; 1.7 HelmholtzWeyl Decomposition; 1.8 Comments; 2. Linear Stationary Problem; 2.1 Existence and Uniqueness of Weak Solutions; 2.2 Coercive Estimates; 2.3 Local Regularity; 2.4 Further Local Regularity Results, n = 2, 3; 2.5 Stokes Operator in Bounded Domains; 2.6 Comments; 3. NonLinear Stationary Problem; 3.1 Existence of Weak Solutions
 3.2 Regularity of Weak Solutions3.3 Comments; 4. Linear NonStationary Problem; 4.1 Derivative in Time; 4.2 Explicit Solution; 4.3 Cauchy Problem; 4.4 Pressure Field. Regularity; 4.5 Uniqueness Results; 4.6 Local Interior Regularity; 4.7 Local Boundary Regularity; 4.8 Comments; 5. Nonlinear NonStationary Problem; 5.1 Compactness Results for NonStationary Problems; 5.2 Auxiliary Problem; 5.3 Weak LerayHopf Solutions; 5.4 Multiplicative Inequalities and Related Questions; 5.5 Uniqueness of Weak LerayHopf Solutions. 2D Case; 5.6 Further Properties of Weak LerayHopf Solutions
 Appendix A Backward Uniqueness and Unique ContinuationA. 1 CarlemanType Inequalities; A.2 Unique Continuation Across Spatial Boundaries; A.3 Backward Uniqueness for Heat Operator in Half Space; A.4 Comments; Appendix B LemarieRiesset Local Energy Solutions; B.1 Introduction; B.2 Proof of Theorem 1.6; B.3 Regularized Problem; B.4 Passing to Limit and Proof of Proposition 1.8; B.5 Proof of Theorem 1.7; B.6 Density; B.7 Comments; Bibliography; Index
 Control code
 894894804
 Dimensions
 unknown
 Extent
 1 online resource
 File format
 unknown
 Form of item
 online
 Isbn
 9789814623414
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number
 (OCoLC)894894804
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